Margin requirement determination and modeling for cleared credit

ABSTRACT

Systems and methods are provided for calculating margin requirements and stress testing exposures of cleared credit portfolios. These margin requirements are calculated using the following components: spread risk, idiosyncratic risk, interest rate, and liquidity risk. The calculation of these risk components is accomplished with a detailed statistical analysis of the risk factors underlying instruments, such as a credit default swap instrument.

CROSS-REFERENCES TO RELATED APPLICATIONS

This application is a continuation under 37 C.F.R. § 1.53(b) of U.S.patent application Ser. No. 14/706,673, filed May 7, 2015, which, inturn, claimed priority to Provisional Application, U.S. Ser. No.61/994,624, filed May 16, 2014, and to Provisional Application, U.S.Ser. No. 61/994,611, filed May 16, 2014, the entire disclosures of whichare all incorporated herein by reference and relied upon.

FIELD OF THE INVENTION

Aspects of the invention relate to determining risks and marginrequirements. More particularly, aspects of the invention relate todetermining costs associated with liquidity margin requirements using arisk model for cleared credit.

BACKGROUND

Exchanges are typically associated with clearing houses that areresponsible for settling trading accounts, clearing trades, collectingand maintaining performance bond funds, regulating delivery andreporting trading data. Clearing is the procedure through which theclearing house becomes buyer to each seller of a contract, and seller toeach buyer, and assumes responsibility for protecting buyers and sellersfrom financial loss by assuring performance on each contract. This iseffected through the clearing process, whereby transactions are matched.

Clearing houses establish clearing level performance bonds (margins) fortraded financial products and establishes minimum performance bondrequirements for customers. A performance bond, also referred to as amargin, is the funds that may be required to deposited by a customerwith his or her broker, by a broker with a clearing member or by aclearing member with the clearing house, for the purpose of insuring thebroker or clearing house against loss on open contracts. The performancebond is not a part payment on a purchase and helps to ensure thefinancial integrity of brokers, clearing members and exchanges or othertrading entities as a whole. A performance bond to clearing house refersto the minimum dollar deposit which is required by the clearing housefrom clearing members in accordance with their positions. Maintenance,or maintenance margin, refers to a sum, usually smaller than the initialperformance bond, which must remain on deposit in the customer's accountfor any position at all times. In order to minimize risk to an exchangeor other trading entity while minimizing the burden on members, it isdesirable to approximate the requisite performance bond or marginrequirement as closely as possible to the actual risk of the account atany given time.

Risks and margin requirements can be difficult to determine for illiquidand concentrated positions. Illiquid positions do not allow a clearinghouse to quickly liquidate positions, which makes it difficult to valuerisks. Concentrated positions can make it difficult for a clearing houseor other entity to find a buyer or seller. Accordingly, there is a needin the art for systems and methods for determining risks and marginrequirements for illiquid and concentrated positions.

SUMMARY OF THE INVENTION

Aspects of the invention overcomes at least some of the problems andlimitations of the prior art by providing systems and methods forvaluing risks and margin requirements for portfolios that are illiquidor have concentrated positions. In some cases a model may include one ormore of the following components: spread risk requirement, idiosyncraticrisk requirement, interest rate requirement, and liquidity riskrequirement. The choice, calibration and calculation of these riskrequirements may dwell on a detailed statistical analysis of the riskfactors underlying financial instruments in a portfolio. The proposedrisk model may use daily log changes in credit spreads as spread riskfactors. For single names the spread changes may be calculated for thestandard benchmark tenors at 1, 3, 5, 7, and 10 years. For indices,which are quoted at fixed maturities, fixed tenor spread changes arebootstrapped from synthetic run rank series at fixed tenors to alignwith the single names. The new model may not rely on decomposition ofindices into their single name constituents.

In some embodiments of the invention the concentration based liquiditycharge includes the sum of a concentration charge for market exposureand a concentration charge for the basis of the portfolio.

In other embodiments, the present invention can be partially or whollyimplemented on a computer-readable medium, for example, by storingcomputer-executable instructions or modules, or by utilizingcomputer-readable data structures.

Of course, the methods and systems of the above-referenced embodimentsmay also include other additional elements, steps, computer-executableinstructions, or computer-readable data structures. In this regard,other embodiments are disclosed and claimed herein as well.

The details of these and other embodiments of the present invention areset forth in the accompanying drawings and the description below. Otherfeatures and advantages of the invention will be apparent from thedescription and drawings, and from the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention may take physical form in certain parts and steps,embodiments of which will be described in detail in the followingdescription and illustrated in the accompanying drawings that form apart hereof, wherein:

FIG. 1 shows an illustrative trading network environment forimplementing trading systems and methods according to at least someembodiments;

FIG. 2 shows an illustrative liquidity charge computing device that maybe used to implement a liquidity model for cleared credit according toat least some embodiments;

FIG. 3 shows an illustrative method for determining a liquidity chargeaccording to at least some embodiments;

FIGS. 4 and 5 show illustrative charts for calibrating an aspect of theliquidity charge associated with a credit default swap according to atleast some embodiments; and

FIGS. 6-10 show illustrative charts showing an impact on margin accountsaccording to at least some embodiments;

FIG. 11 shows an illustrative block diagram of a clearinghouse computingsystem for generating and applying a risk model to determine marginrequirements of a credit default swap portfolio according to at leastsome embodiments;

FIG. 12 shows an illustrative method for generating a model fordetermining margin for a credit default swap portfolio according to atleast some embodiments;

FIG. 13 shows an illustrative risk factor calibration system for use ingenerating a risk model according to at least some embodiments;

FIGS. 14 and 15 show an illustrative method for determining a totalspread risk requirement for a risk model of a CDS portfolio according toat least some embodiments;

FIG. 16 shows an illustrative profit and loss distribution of a riskmodel according to at least some embodiments;

FIG. 17 shows an illustrative backtesting framework for testing a riskmodel for a CDS portfolio according to at least some embodiments;

FIG. 18 shows an illustrative block diagram representation of an riskfactor scenario generator according to at least some embodiments;

FIG. 19 shows an illustrative method for determining an interest ratesensitivity charge according to at least some embodiments.

FIGS. 20-22 show charts illustrative of a margin impact based on therisk model for a CDS portfolio according to at least some embodiments;

FIGS. 23-24 show illustrative backtesting results of historicalportfolio information based on the risk model according to at least someembodiments; and

FIG. 25 shows an illustrative margin break percentage of gross notionaland an illustrative spread risk requirement break percentage of grossnotional per a number of occurrences based on the risk model accordingto at least some embodiments.

DETAILED DESCRIPTION

In some cases, a risk model may be used for risk management pertainingto clearing of Credit Default Swap (CDS) and related instruments,including but not limited to NA CDX indices, NA single names, iTraxxindices, iTraxx single names, other credit indices, futures on indices,etc.

A clearing house may rely on one or more models to calculate marginrequirements for its cleared credit portfolios. For example, theclearing house may provide clearing services for North American (NA)indices (IG and HY), foreign indices (e.g., Itraxx, etc.), NA singlenames, and/or foreign single names. As part of the clearing services,the clearinghouse may calculate margin requirements and/or stress testexposures to feed guarantee fund calculations. These calculations mayrely on a risk management model that conforms to regulatory requirementsand to the risk appetite of the clearing house. A risk model maybedesired to provide good coverage across a representative set ofportfolios under a comprehensive set of historical and hypotheticalscenarios, take into account all of the significant risk factorsrelevant to CDS instruments, consistently and proportionately model theeffect of relevant risk factors on the total risk exposure of creditportfolios, and have robust, intuitive and justifiable parameterizationthat supports a reliable and transparent calibration and replicationprocess.

Currently an illustrative clearing house may rely on models, such as asix factor model, to calculate margin requirements and may use amodified version of the model, to calculate stress requirements for itscleared credit portfolios. An illustrative current six-factor model mayinclude systematic components, convergence/.divergence components,sector components, curve components, idiosyncratic components, andliquidity components. Often, however, a focus of the model may be on themargin model and/or the stress model without using liquidity. Further,the stress model may be modified to use a subset of the components ofthe margin model, such as a maximum four of the first five componentslisted for the margin model with or without liquidity. By using separatemodels, the calibration of the components may be different for marginand stress calculations. Further, the model may not handle indicesdirectly, but may rely on decomposition of the indices into their singlename constituents for profit and loss (P&L) calculations under shockscenarios.

However, the current risk models may not lead to an optimal and/orefficient assessment of credit portfolio risk. Further, these currentrisk models may have gross notional based charges (curve component) thatare agnostic to portfolio risk characteristics. As a result, thecalibration process may result in double counting of risk and may notappropriately take into account the effect of margin period of risk.This model parameterization, together with improper calibration, maylead to very static margins that are not reactive to changing marketconditions. Further, the current model may have serious scalabilityissues due to lack of explicit correlation modeling. Furthermore, theinconsistencies in stress and margin calculations may lead tounintuitive changes in portfolio risk as a result of changes in theportfolio decomposition.

In some cases, an illustrative risk model for cleared credit (RMCC) maybe used to overcome the above-noted deficiencies of many currently usedmodels. The RMCC may be based on and/or supported by salientcharacteristics of risk factors affecting credit portfolios. The RMCCmay be efficient in modeling risk of a portfolio of credit derivatives.For example, the RMCC may account for effects of hedging,diversification and concentration. Further, the risk model for clearedcredit may be reactive to current market conditions and may bepersistent to extreme events. The RMCC may be configured to beconsistent with one or more risk policies, such as a margin period ofrisk. In some cases, the RMCC may be further configured to includespecified add-ons for out of model conditions.

By using a risk modeling system, the clearinghouse may use an RMCC toprovide a simple and/or intuitive model that may produce results thatare easy to replicate by end users due to intuitive and/orstraightforward parameterization. Further, this RMCC may be applicableto a broad range of instruments, such as CDX NA Indices for high yield(HY) and investment grade (IG) products, iTraxx (e.g., European, Asian,etc.) indices other credit indices, and to North American single namesand/or foreign single names. The RMCC may include a clear calibrationprocess that may be used to provide stability of the model parametersover time and/or to justify all model parameters based, at least inpart, on empirical data. This risk model may be flexible enough to offercross asset offsets and may be suitable for offering portfolio marginingwith correlated instruments. In some cases, the risk model may includecounter-cyclical parameters, such as those used in counter cyclicalvolatility and correlation modeling (e.g., a long-run historicalvolatility floor, a systemic correlation scenario, a basis correlationscenario, etc.). Further, the risk model may be readily extendible tostress calculations.

Aspects of the present invention are implemented with computer devicesand computer networks that allow users to exchange trading information.An exemplary trading network environment for implementing tradingsystems and methods is shown in FIG. 1. An exchange computer system 100receives orders and transmits market data related to orders and tradesto users. Exchange computer system 100 may be implemented with one ormore mainframe, desktop or other computers. A user database 102 includesinformation identifying traders and other users of exchange computersystem 100. Data may include user names and passwords. An account datamodule 104 may process account information that may be used duringtrades. A match engine module 106 is included to match bid and offerprices. Match engine module 106 may be implemented with software thatexecutes one or more algorithms for matching bids and offers. A tradedatabase 108 may be included to store information identifying trades anddescriptions of trades. In particular, a trade database may storeinformation identifying the time that a trade took place and thecontract price. An order book module 110 may be included to compute orotherwise determine current bid and offer prices. A market data module112 may be included to collect market data and prepare the data fortransmission to users. A risk management module 134 may be included tocompute and determine a user's risk utilization in relation to theuser's defined risk thresholds. An order processing module 136 may beincluded to decompose delta based and bulk order types for processing byorder book module 110 and match engine module 106.

The trading network environment shown in FIG. 1 includes computerdevices 114, 116, 118, 120 and 122. Each computer device includes acentral processor that controls the overall operation of the computerand a system bus that connects the central processor to one or moreconventional components, such as a network card or modem. Each computerdevice may also include a variety of interface units and drives forreading and writing data or files. Depending on the type of computerdevice, a user can interact with the computer with a keyboard, pointingdevice, microphone, pen device or other input device.

Computer device 114 is shown directly connected to exchange computersystem 100. Exchange computer system 100 and computer device 114 may beconnected via a T1 line, a common local area network (LAN) or othermechanism for connecting computer devices. Computer device 114 is shownconnected to a radio 132. The user of radio 132 may be a trader orexchange employee. The radio user may transmit orders or otherinformation to a user of computer device 114. The user of computerdevice 114 may then transmit the trade or other information to exchangecomputer system 100.

Computer devices 116 and 118 are coupled to a LAN 124. LAN 124 may haveone or more of the well-known LAN topologies and may use a variety ofdifferent protocols, such as Ethernet. Computers 116 and 118 maycommunicate with each other and other computers and devices connected toLAN 124. Computers and other devices may be connected to LAN 124 viatwisted pair wires, coaxial cable, fiber optics or other media.Alternatively, a wireless personal digital assistant device (PDA) 122may communicate with LAN 124 or the Internet 126 via radio waves. PDA122 may also communicate with exchange computer system 100 via aconventional wireless hub 128. As used herein, a PDA includes mobiletelephones and other wireless devices that communicate with a networkvia radio waves.

FIG. 1 also shows LAN 124 connected to the Internet 126. LAN 124 mayinclude a router to connect LAN 124 to the Internet 126. Computer device120 is shown connected directly to the Internet 126. The connection maybe via a modem, DSL line, satellite dish or any other device forconnecting a computer device to the Internet.

One or more market makers 130 may maintain a market by providingconstant bid and offer prices for a derivative or security to exchangecomputer system 100. Exchange computer system 100 may also exchangeinformation with other trade engines, such as trade engine 138. Oneskilled in the art will appreciate that numerous additional computersand systems may be coupled to exchange computer system 100. Suchcomputers and systems may include clearing, regulatory and fee systems.

The operations of computer devices and systems shown in FIG. 1 may becontrolled by computer-executable instructions stored oncomputer-readable medium. For example, computer device 116 may includecomputer-executable instructions for receiving order information from auser and transmitting that order information to exchange computer system100. In another example, computer device 118 may includecomputer-executable instructions for receiving market data from exchangecomputer system 100 and displaying that information to a user.

Of course, numerous additional servers, computers, handheld devices,personal digital assistants, telephones and other devices may also beconnected to exchange computer system 100. Moreover, one skilled in theart will appreciate that the topology shown in FIG. 1 is merely anexample and that the components shown in FIG. 1 may be connected bynumerous alternative topologies.

Illustrative Embodiments

In some cases, a risk model for cleared credit (RMCC) may be processedby a clearinghouse computer system using a combination of differentfactors. For example, the clearinghouse computer system may process theRMCC using a spread risk module to process a spread risk component, anidiosyncratic risk module to process an idiosyncratic risk component, aninterest rate module to process an interest rate risk component and aliquidity risk module to process a liquidity risk component. Thesecomponents may be chosen, calibrated and calculated based on astatistical analysis of the risk factors underlying CDS instruments.

Liquidity Risk Requirement and Model

In some cases, a risk model may be used for risk management pertainingto clearing of Credit Default Swap (CDS) and related credit instruments,including but not limited to NA CDX indices, NA single names, iTraxxindices, iTraxx single names, other credit indices, futures on indices,etc.

Sources of risks arising from clearing credit default swaps may includethe cost of liquidating the CDS portfolio of a clearing member firm incase of default. Efficient modeling and estimation of this cost may beas important as quantifying the market risk related costs, if not more,for credit instruments as these instruments do have varying degrees ofliquidity characteristics. A clearing house may offer clearing servicesfor different indices, such as NA indices (IG and HY) and is planning toextend its offering to iTraxx indices (Main, Cross Over), and NorthAmerican and European single names. The calculation of liquidity riskrequirements as part of margin and stress exposures may be important tothe success of a risk management model that conforms to regulatoryrequirements and to the risk appetite of the Clearing House. Theliquidity risk model may, therefore, be used to provide good coverageacross a representative set of portfolios under a comprehensive set ofhistorical and hypothetical scenarios representing distressed liquidity,to take into account liquidity characteristics of credit instrumentsbased on contract tenors, index families and series, and referenceentities. In some cases, the liquidity risk model may also be used toconsistently and proportionately model the effect of concentration(position size), to have a robust, intuitive and justifiableparameterization that supports a reliable and transparent calibrationand replication process, and to be consistent with a default managementprocess.

In some cases, a liquidity model used by an illustrative clearing housemay address liquidity risk of portfolios consisting of only NA indices(IG and HY). In some cases, the current liquidity requirement mayinclude two components which are intended to cover the costs associatedwith the steps of a typical liquidation process. The first component maybe designed to cover the cost of hedging the market exposure of adefaulted portfolio while the second component may address the cost ofliquidating the hedged portfolio. A progressive concentration charge mayimplicitly embed into the liquidity requirement through a super-lineardependence on position size. The Bid/Ask data across different seriesand tenors of index instruments may be incorporated in the model througha liquidity floor which is intended to address the liquidity risk ofsmaller size portfolios, which may be transacted at observed Bid/Askspreads in case of default.

A previously used risk model may not differentiate between on-the-runand off-the-run indices and/or contracts of different tenors as long asthey have similar market risk exposures measured by their SDV01 (spreadadjusted DV01). The model therefore may not address the drop inliquidity of index series when they become off-the-run and the relativeilliquidity of contracts on non 5-year tenors. This characteristic ofthe model makes it harder to extend to single names and other indexinstruments without making significant adjustments.

FIG. 2 shows an illustrative block diagram representation of a liquiditycharge computing system 200 for implementing a model for determining aliquidity charge associated with a credit default swap (CDS) portfolio.In some cases, the liquidity charge computing system may include aliquidity charge computing device 200 communicatively coupled via anetwork 205 (e.g., a wide area network (WAN), the LAN 124, the Internet126, etc.) to a CDS market computing system 210. The CDS marketcomputing system may include one or more computing devices configuredfor receiving and disseminating information corresponding to a CDSmarket, such as pricing information (e.g., bid information, askinformation, etc.), CDS quality information (e.g., investment gradeinformation, high yield information, etc.), tenor information, and/orthe like. The liquidity charge computing device 210 may becommunicatively coupled to a clearinghouse computing system 240 via thenetwork 205, or otherwise incorporated into the clearinghouse computingsystem 240.

In some cases, the clearinghouse computing system 240 may include a datarepository 242, one or more computing devices 244 and/or a userinterface 246. The data repository may store instructions, that whenexecuted by the one or more computing devices 244, may cause the one ormore computing devices 244 to perform operations associated withdetermining performance bond contributions associated with holdings inproducts that are based on various types of credit default swaps. Insome cases, the clearinghouse computing system 240 may presentperformance bond and/or margining information to a financial institutionvia the network 205, wherein the financial institution holds one or moreportfolios that include a credit default swap. Further, theclearinghouse computing system 240 may further present the performancebond and/or margining information via one or more user interface screensvia the user interface 246. The user interface 246 may be local to theclearinghouse computing system 240 and/or remote from the clearinghousecomputing system 240 and accessible via the network 205. The userinterface screens may graphically and/or textually present informationcorresponding to a margin requirement determined for a CDS portfolio asdetermined by the liquidity charge computing device 210.

The liquidity charge computing device 210 may include a processor 212,one or more non-transitory memory devices 214 (e.g., RAM, ROM, a diskdrive, a flash drive, a redundant array of independent disks (RAID)server, and/or other such device etc.), a user interface 216, a datarepository 218, a communication interface to facilitate communicationsvia the network 205, and/or the like. The liquidity charge computingdevice 210 may be configured to store instructions in the one or morememory devices 214 and/or the data repository 218 that, when executed bythe processor 212, may configure the liquidity charge computing device210 to execute a model for determining margining requirements associatedwith a CDS portfolio. In some cases, the liquidity charge computingdevice 210 may process the instructions stored in the memory device 214and/or the data repository 218 to calculate the margining requirementsusing an outright exposure calculator 220 and/or a basis exposurecalculator 230. In some cases, the outright exposure calculator 220 maybe used to calculate an outright exposure to liquidity charges forholdings held in a CDS portfolio. For example, the outright exposurecalculator 220 may calculate an exposure associated with hedging aninvestment grade (IG) sub-portfolio held in the CDS portfolio using anIG exposure calculator 222. Similarly, the outright exposure calculator220 may calculate an exposure associated with hedging a high yield (HY)sub-portfolio held in the CDS portfolio using a HY exposure calculator224. The basis exposure calculator 230 may be used to calculate a costof unwinding hedged positions held in the CDS portfolio. For example,the basis exposure calculator 230 may process instructions to calculatea cost of unwinding hedged single name positions held in the CDSportfolio using a single name basis exposure calculator 232. Similarly,the basis exposure calculator 230 may process instructions to calculatea cost of unwinding hedged index positions held in the CDS portfoliousing an index basis exposure calculator 234.

The liquidity charge computing device 210 may process instructionscorresponding to model to determine a liquidity charge and/or marginrequirement associated with any particular CDS swap portfolio. Thismodel may be stored as instructions in the one or more non-transitorymemory devices 214 and/or the data repository 218 that, when executed bythe processor 212 may cause the liquidity charge computing device tocalculate the liquidity charge by calculating up to four different termsthat may be added to yield an aggregate liquidity charge for portfoliosconsisting of indices (IG, HY) and single names, such as a cost of SDV01hedge for IG sub-portfolio, a cost of SDV01 hedge for HY sub-portfolio,a cost of unwinding hedged index positions, and a cost of unwindinghedged single name positions. In some cases, the indexes and/or singlename positions may be associated with a North American CDS market and/ora foreign CDS market (e.g., a European CDS market, an Asian CDS market,etc.). In some cases, a single name CDS may be based on a swapassociated with a particular single name (e.g., corporation). An indexmay include a plurality of single name positions. As such, an indexbased CDS may be similar to a futures contract and may be based on avalue of an index at a given time.

The liquidity charge computing device 210 may calculate a costassociated with liquidating the CDS positions held in a particular CDSportfolio. This liquidity charge may be used when determining marginrequirements for the accounts holding one or more CDS portfolios. Theliquidity charge may be calculated by the outright exposure calculator220 and the basis exposure calculator of the liquidity charge computingdevice 210 using the formula:

$\begin{matrix}{{{Liquidity}\mspace{14mu} {Charge}} = {{{Outright}\mspace{14mu} {exposure}} + {{Index}\mspace{14mu} {Basis}\mspace{14mu} {Exposure}} + {{Single}\mspace{14mu} {Name}\mspace{14mu} {Basis}\mspace{14mu} {Exposure}}}} & (1) \\{\mspace{20mu} {{where},}} & \; \\{{{{IG}\mspace{14mu} {Outright}\mspace{14mu} {Exposure}} = {\alpha_{IG}{{{SDV}\; 01_{IG}}}\max \left\{ {{\frac{{SDV}\; {01_{IG}/{SDV}}\; 01_{{OTR},{IG},{5Y}}}{{w\left( {5Y} \right)}\gamma \; Q_{0,{OTR},{IG},{5Y}}}}^{1.5},1} \right\}}},} & (2) \\{\mspace{20mu} {{{where}\mspace{14mu} {SDV}\; 01_{IG}} = {\sum_{\underset{\tau \in {({1,3,5,7,10})}}{{i \in {IG}},{{IN}\mspace{11mu} {and}\mspace{14mu} {SN}}}}{{SDV}\; 01_{i}}}}} & (3) \\{{{{HY}\mspace{11mu} {Outright}\mspace{14mu} {Exposure}} = {\alpha_{HY}{{{SDV}\; 01_{HY}}}\max \left\{ {{\frac{{SDV}\; {01_{HY}/{SDV}}\; 01_{{OTR},{HY},{5Y}}}{{w\left( {5Y} \right)}\gamma \; Q_{0,{OTR},{HY},{5Y}}}}^{1.5},1} \right\}}},} & (4) \\{\mspace{20mu} {{{where}\mspace{14mu} {SDV}\; 01_{HY}} = {\sum_{\underset{\tau \in {({1,3,5,7,10})}}{{i \in {HY}},{{IN}\mspace{14mu} {and}\mspace{14mu} {SN}}}}{{SDV}\; 01_{i}}}}} & (5) \\{{{Index}\mspace{14mu} {Basis}\mspace{14mu} {Exposure}} = {\beta_{IN}{\sum_{\underset{\underset{{- {HY}}\mspace{14mu} {OTR}\mspace{11mu} 5Y}{{- {IG}}\mspace{14mu} {OTR}\mspace{14mu} 5Y}}{{i \in {IN}},{\tau \in {({1,3,5,7,10})}}}}{{f(\tau)}{{{SDV}\; 01_{i\; \tau}}}\max \left\{ {{{{Q_{i}/{w(\tau)}}\gamma \; Q_{0i}}}^{0.5},1} \right\}}}}} & (6) \\{{{Single}\mspace{14mu} {Name}\mspace{14mu} {Basis}\mspace{14mu} {Exposure}} = {\beta_{SN}{\sum_{\underset{\tau \in {({1,3,5,7,10})}}{{i \in {SN}},}}{{f(\tau)}{{{SDV}\; 01_{i\; \tau}}}\max \left\{ {{{{Q_{i}/{w(\tau)}}\gamma \; Q_{0i}}}^{0.5},1} \right\}}}}} & (7)\end{matrix}$

Here, Q_(0i) is a median weekly trading volume and may be calibrated tomost recent 13 weeks for the entity (e.g., single name) and aggregatedacross different tenors. Q_(0i) is a median weekly trading volume andmay be calibrated to most recent 13 weeks for the entity (e.g., singlename) and aggregated across different tenors. The function f(τ) is atenor scalar for calculating the liquidity charge and may be based on aratio of Bid-Ask/Mid prices across different tenors. The function w(τ)is a tenor adjustor for weekly trading volume and may be a function off(τ). The constant γ is associated with a proportion of weekly tradingvolume that can be liquidated per day. This constant may be set to anyvalue and may be set to a same value for the different sub portfolios(e.g., HY, IG) and/or for index basis exposure and/or single name basisexposure. For example, γ may be set to a particular constant value foreach equation (2), (4), (6), and (7) (e.g., about 10%, about 15%, about5%, etc.). In some cases, γ may be set to different values whendetermining the IG or HY outright exposure, the Index basis exposure,and/or the single name basis exposure.

In an illustrative example, the cost of an SDV01 hedge for an IGsub-portfolio may represent the cost of hedging the aggregate SDV01exposure of IG indices and IG single names. This cost may be measured asa function of the IG on-the-run notional required for hedging the totalSDV01 exposure of the IG sub-portfolio. The charge scales super linearlywhen the hedge notional may become relatively large compared to aproportion (e.g., about 10%) of the median weekly trading volume ofon-the-run IG 5-year contract. The trading volume on the 5-year contractmay be estimated by applying a tenor adjustor on the total tradingvolume of the on-the-run IG contracts. The tenor adjustor may becalibrated to Bid/Ask and Mid spread data on indices.

The cost of an SDV01 hedge for an HY sub-portfolio may represent thecost of hedging the aggregate SDV01 exposure of HY indices and HY singlenames. This cost may be measured as a function of the HY on-the-runnotional required for hedging the total SDV01 exposure of the HYsub-portfolio. The charge may scale super linearly when the hedgenotional becomes relatively large compared to a proportion (e.g., about10%) of the median weekly trading volume of on-the-run HY 5-yearcontract. The trading volume on the 5-year contract may be estimated byapplying a tenor adjustor on the total trading volume of the on-the-runHY contracts. The tenor adjustor may be calibrated to Bid/Ask and Midspread data on indices.

A cost of unwinding hedged index positions may represent the cost ofliquidating hedged index positions. This cost may be measured as afunction of the SDV01 of each off-the-run or non-5 year index seriesposition. The charge may scale super linearly when the position notionalbecomes relatively large compared to a proportion (e.g., about 10%) ofthe median weekly trading volume of the index series and tenorcombination. The trading volume of the index series and tenor may beestimated by applying a tenor adjustor on the total trading volume ofthe index series. The tenor adjustor may be calibrated to Bid/Ask andMid spread data on indices.

A cost of unwinding hedged single name positions may represent the costof liquidating single name positions of the CDS portfolio hedged bycorresponding index positions. This cost may be measured as a functionof the SDV01 of each single name position. The charge may scale superlinearly when the position notional becomes relatively large compared toa proportion (e.g., about 10%) of the median weekly trading volume ofthe reference entity and tenor combination. The trading volume of thereference entity and tenor may be estimated by applying a tenor adjustoron the total trading volume of the reference entity. The tenor adjustormay be calibrated to Bid/Ask and Mid spread data on single names.

The liquidity model may include a number of risk aversion parameters,(e.g., four risk aversion parameters as illustrated) which may beassociated with different terms in the liquidity formula. These riskaversion parameters may be calibrated and/or back-tested to dealer pollson liquidity. For example, the risk aversion parameters may becalibrated to account for pure index CDS portfolios and/or for singlename CDS portfolios. The single name CDS portfolios may include indexpositions to cover index-single name arbitrage portfolios, and/or thelike.

While the model illustrated in equations (1)-(7) may be configured tocover liquidity exposure (e.g., risk) associated with North American(e.g., NA) CDS markets, the model can easily be extended to cover aliquidity risk of portfolios that may contain other indices (e.g., aEuropean CDS index, an Asian CDS index, etc.) such as iTraxx. Theextension of the model to cover other product families may be achievedsimply by adding terms for hedging and unwinding such positions (afterhedging). Calibration of the risk aversion parameters for these termsmay be done using dealer polls on portfolios containing suchinstruments.

The model for liquidity charge for CDS portfolios, as executed by theoutright exposure calculator 220 and the basis exposure calculator 230of the liquidity charge computing device, may distinguish betweenon-the-run/off-the-run indices and single names based on trading volumedata, where the different credit default swaps have different levels ofliquidity. The model may also differentiate between outright and market(e.g., risk) neutral portfolios, account for an effect of tenorsassociated with different CDS swaps held in the portfolio on liquidity,and may scale super-linearly (e.g., a 1.5 exponential equation) as afunction of notional to account for a concentration of risk. In somecases, the model may incorporate weekly trading volume data from theDepository Trust & Clearing Corporation (DTCC), to differentiate betweencorporate obligors, on-the-run indexes, and/or off-the-run indexes. Insome cases, the model may account for an effect of tenor on liquidity.

FIG. 3 shows an illustrative method 300 for determining a liquiditycharge according to aspects of this disclosure. As discussed above, theliquidity charge computing device 210 may process instructions tocalculate a liquidity charge, such as by using equation (1) discussedabove. For example, at 310, the outright exposure calculator 220 maycalculate a cost associated with a SDV01 hedge corresponding to an IGsub-portfolio of a CDS portfolio. Similarly, at 320, the outrightexposure calculator 220 may calculate a cost associated with a SDV01hedge corresponding to a HY sub-portfolio o the CDS portfolio. Forexample, a scalar value (e.g., α, β, etc.) may be calibrated to one ormore dealer polls associated with the representative CDS portfolios. Insome cases, the SDV01 hedge value may be calculated at the CDS portfoliolevel, such as by determining an SDV01 for each position of theportfolio. The SDV01 may be a measure of sensitivity of each CDS to a 1%change in a power spread curve corresponding to the contract. The IGexposure calculator 222 may calculate the exposure for the IGsub-portfolio based on a SDV01 determined based on an on-the-run CDSswap having a 5-year tenor. This SDV01 (SDV01_(IG)) may be used todetermine an amount of notional corresponding to the on-the-run, 5-yearCDS required to hedge the SDV01 exposure of the overall IGsub-portfolio. In some cases, a CDS may roll periodically (e.g., March,September), and in such cases, the calculations will roll (e.g., bebased on) the new series. In some cases, an adjustment value, w(τ) maybe used to calibrate the calculation based on a particular tenor (e.g.,a 5-year tenor). This adjustment value may be calibrated based on dealersurveys on a periodic (e.g., semi-annual) basis. In some cases, such asfor large CDS portfolios, the IG outright exposure may scalesuper-linearly, such as by a factor of 1.5. In other cases, such as forsmall CDS portfolios, the IG outright exposure may scale linearly, suchas by using a maximum value. Additionally, the outright exposurecalculator may further scale the outright exposure using a mediantrading volume parameter, such as a trading volume as reported by theDTCC.

At 330, the liquidity charge computing device 210 may calculate a costassociated with unwinding one or more hedged index positions associatedwith the CDS portfolio, such as by using the basis exposure calculator230. At 340, the liquidity charge computing device 210 may calculate acost associated with unwinding one or more hedged single name positionsassociated with the CDS portfolio, such as by using the basis exposurecalculator 230. At 350, the liquidity charge computing device 210 maycalculate a liquidity charge associated with the CDS portfolio based onthe cost of the SDV01 hedge of the IG sub-portfolio and the cost of theSDV01 hedge of the HY sub-portfolio, the cost of unwinding the hedgedindex positions and the cost of unwinding the hedged single namepositions. In some cases, the liquidity charge computing device 210 maycommunicate the calculated liquidity charge via the network 205 to theclearinghouse computing system 240. The clearinghouse computing system240 may use the liquidity charge in one or more calculations todetermine margining requirements corresponding the CDS portfolio. Theclearinghouse computing system 240 may further communicate the marginingrequirements to an account owner of the account containing the CDSportfolio and/or a financial institution associated with the CDSportfolio.

FIGS. 4 and 5 show illustrative charts 400, 500 for calibrating anaspect of the liquidity charge associated with a credit default swapportfolio. In chart 400, a ratio of (Bid-Ask/Mid) values associated witha particular tenor (e.g., 1-year, 3-year, 5-year, 7 year, 10-year, etc.)are compared to a value of a (Bid-Ask/Mid) ratio associated with a5-year tenor over one or more different run-rank series. The surface 410represents the ratio (e.g., f(τ) 415) across the different tenors 420and different run ranks 425. The run ranks correspond to an on-the-runseries (e.g., 0) and different off-the-run series (e.g., −1 year, −2year, etc.). The chart 500 shows an illustrative (Bid-Ask/Mid) ratiof(τ) 415 associated with different tenors 420 over a particular run-rankseries, such as the on-the-run series.

In some cases, these ratios for indexes may be calibrated to recent(e.g., weekly, monthly, semiannual, etc.) poll results and ratios forsingle names may be calibrated to historical data. For example, ratiosfor single name credit default swaps may be calibrated to historicalpoll data during a specified time frame, such as by using a precedingyear's poll results. In some cases, additional calibration may be doneby calculating a run-rank specific tenor scalar function for indexesand/or by polling on single name bid/ask spreads across tenors forcalibration of single name tenor dependence, and/or the like.

FIGS. 6-10 show illustrative charts showing an impact on margin accountsbased on use of a model according to aspects of the invention. Forexample, FIG. 6 shows an illustrative chart 600 representing a marginimpact on a house account of a plurality of clearing member firms 605.An illustrative chart 650 represents a margin impact on aggregatecustomer accounts for a plurality of clearing member firms 605. For eachfirm, margin and liquidity 610 are shown based on calculations using aprevious model and new margin and new liquidity 620 are shown based onthe model discussed above, as implemented using the liquidity chargecomputing device 210. Additionally, for each of the clearing memberfirms 605, a change in total margin 630 is shown between the margin andliquidity 610 calculated using the previous model and the new margin andnew liquidity 620 calculated using the new model. As can be seen inchart 600, for house accounts, margin requirements including liquiditycharges, have been reduced using the new model by at least 10%, with anaverage of about a 30% reduction in margin costs. For customer accounts,margin requirements including liquidity charges have mostly been reducedfrom about 2% to about 10%.

Chart 700 of FIG. 7 shows an impact of liquidity margin across marginaccounts as a ratio of the newly calculated liquidity margin to theliquidity margin calculated using a previous model. As can be seen, inmany cases, liquidity margin has increased using the new model. As canbe seen in chart 750, the largest increases 760 in total margin havebeen seen in credit default swaps having the most associated liquidityrisks, such as in off-the-run HY or outright 10Y positions.

FIGS. 8 and 9 show illustrative charts 800, 900 illustrating changesseen in the margin accounts for firm 6 and firm 12 using the liquiditycharges calculated by the liquidity charge computing device 210. Forexample, for both firm 6 and firm 12, margins without liquidity havedecreased significantly due to decommissioning of the gross notionalbased curve charge. Also, for both firms, liquidity margins haveincreased significantly due to off-the-run positions held in theirrespective portfolios. Because firm 12 has more relative exposure tooff-the-run indexes, the liquidity margin increases more than theliquidity margin increase seen by firm 6.

FIG. 10 shows an illustrative chart 1000 showing a rolling effect seenin margin and liquidity requirements. For example, Firm 7 has arelatively hedged portfolio with concentrated positions in IG 18 and IG20 CDS positions. The liquidity charge, as calculated using equation 1by the liquidity charge computing device 210, drops significantly whenthe concentrated positions are rolled to IG 20 and IG 21 CDS positions.Previously, using other methods, the liquidity charge is unaffected bythe roll.

Risk Model for Cleared Credit Implementation

In at least some embodiments, the exchange computer system 100 mayreceive, store, generate and/or otherwise process data to facilitatemodeling risk associated with financial products, such as cleared creditfinancial products, such as credit default swaps. An illustrativemodeling method for calculating margin implemented by the exchangecomputer system 100 may include multiple components, such as a computerdevice calculating a spread risk requirement, a computer devicecalculating an idiosyncratic risk requirement, a computer devicecalculating an interest rate requirement, and a computer devicecalculating a liquidity risk requirement. The choice, calibration andcalculation of these risk requirements may rely on a detailedstatistical analysis of the risk factors underlying instruments, such ascredit default swap (CDS) instruments. The illustrative risk model(e.g., the RMCC) may be implemented by the exchange computer system 100to use daily log changes in credit spreads as spread risk factors. Forsingle names the spread changes may be calculated for the standardbenchmark tenors at 1, 3, 5, 7, and 10 years. In some cases, the RMCCmay include both a margin model and a stress model, where each modelincluded in the RMCC may be implemented by a computing device includedin the exchange computing system.

FIG. 11 shows an illustrative block diagram of the clearinghousecomputing system 240 for generating and applying a risk model todetermine margin requirements of a credit default swap portfolioaccording to at least some embodiments. In some cases, the clearinghousecomputing system 240 may be configured to implement the clearinghousemodule 140 of the exchange computing system 100. As discussed above, theclearinghouse computing system 240 may include the data repository 242,the one or more computing devices 244 and/or the user interface 246. Insome cases, the clearinghouse computing system 240 may further includethe processor 1147 and the memory 1148, which may be incorporated withinthe one or more computing devices 244 or within another computingdevice, such as a risk modeling computing system 1110. In some cases,the risk model generator 110 may be configured to retrieve instructionsstored in the memory 1148 to be processed by the processor 1147 toimplement one or more aspects of the risk model for cleared credit. Forexample, the risk modeling computer system 1110 may include a spreadrisk factor calculator 1120, an idiosyncratic risk factor calculator1130, a liquidity risk factor calculator 1140 (e.g., the liquidity riskcalculator 210 discussed above) and/or an interest rate factorcalculator 1150. In some cases, the spread risk factor calculator 1120of the risk modeling computing system 1110 may further include a riskfactor scenario generator 1125 to determine a total spread riskrequirement of the RMCC. In some cases, the risk modeling computersystem 1110 may include a margin calculator 1160 that may processinstructions for calculating a margin requirement of a portfolio ofcredit default swaps or a portion of a portfolio including one or morecredit default swaps. The risk modeling computer system 1110 may furtherbe used for performing stress calculations on one or more cleared creditproducts, such as a portfolio including single name credit defaultsswaps and/or index credit default swaps.

The risk modeling computing system 1110 may be communicatively coupledto the user interface 246, which may be local to the clearinghousecomputing system 240 and/or remote from the clearinghouse computingsystem. In such cases, the user interface 246 may present data receivedfrom the risk modeling computing system 1110 using one or more userinterface screens that may be loaded from a data repository, such as thedata repository 242. The risk modeling computing system 1110 may beconfigured to format information output by one or more of the spreadrisk factor calculator 1120, the idiosyncratic risk factor calculator1130, the liquidity risk factor calculator 1140 and/or the interest ratefactor calculator 1150. In some cases, the risk modeling computingsystem 1110 may format the data output into a form (e.g., text,graphics, a combination of text and graphics, etc.) as defined by aparticular user interface screen. In some cases, the risk modelingcomputing system 1110 may be configured to receive, via a communicationsnetwork, information for use in determining the RMCC, performing stresstests on the RMCC, and/or for one or more calibration processes. Suchinformation may be received from a user via the user interface and/orreceived from a remote computer system (e.g., the CDS market computingsystem 230, such as receiving information corresponding to a creditdefault market, such as pricing information, tenor information, interestrate information and the like.

The data repository 242 may store instructions, that when executed bythe one or more computing devices 244, may cause the one or morecomputing devices 244 to perform operations associated with determiningperformance bond contributions associated with holdings in products thatare based on various types of credit default swaps. In some cases, theclearinghouse computing system 240 may present performance bond and/ormargining information based on the calculations performed by the riskmodeling computing system 1110 to a financial institution via thenetwork 205, wherein the financial institution holds one or moreportfolios that include a credit default swap. Further, theclearinghouse computing system 240 may further present the performancebond and/or margining information via one or more user interface screensvia the user interface 246. The user interface screens may graphicallyand/or textually present information corresponding to a marginrequirement determined for a CDS portfolio as determined by the riskmodeling computing system 1110.

In some cases, the margin model of the RMCC may allow for a clear modelcalibration process to be performed by the exchange computing system 100that may lead to stability of the model parameters over time. Forexample, the exchange computing system 100 may process instructions thatset forth clear policies regarding parameter calibration and/or byjustifying all model parameters based on empirical data, such as byliquidity charge computing device 210 as discussed above in reference toFIGS. 1-10. A portfolio level liquidity model may be included in theRMCC and may be applicable to both single names and indices. Unlike someexisting liquidity models, this liquidity model may be applicable toboth small and/or large portfolios. Further, the liquidity model mayallow for limiting market liquidity in a crisis situation. Further, theRMCC may be flexible enough so that it may offer cross asset offsetsthat may assist in portfolio margining with correlated instruments.

FIG. 12 shows an illustrative method of determining a margin requirementassociated with a portfolio of credit default swaps and/or forperforming a stress evaluation of the portfolio of credit default swapsaccording to one or more embodiments. In some cases, the risk modelingcomputer system 1110 of the clearinghouse computing system 240 may beconfigured to calculate, such as by using the spread risk factorcalculator 1120, a spread risk factor corresponding to a value at risk(VaR) associated with a plurality of correlation scenario sets, such asat 1210. The correlation scenario sets may correspond to characteristicsof at least one of a single name credit default swap or an index creditdefault swap of a portfolio. In some cases, the spread risk factorcalculator 1120 may be configured to model a plurality of risk factorsassociated with the portfolio by evaluating one or more possiblescenarios related to different credit default swaps associated with theportfolio. In some cases, the different possible scenarios may beevaluated using one or more families of equations as part of the riskmodel processed by the risk modeling computing system. For example, thespread risk factor calculator may evaluate a plurality of scenariosusing one or more different methods, such as a Monte Carlo simulation.In some cases, the Monte Carlo simulation may be run for each of theplurality of scenarios to obtain a distribution associated with therisks associated with single name credit default swaps and creditdefault swap indices associated with the portfolio. The Monte Carlosimulation processed by the spread risk factor calculator 1120 may beused to process a plurality of risk factors associated with theportfolio with one or more degrees of freedom (e.g., 2, 3, 4, 5, etc.).In some cases, the Monte Carlo simulation may include one or morestudent t-copulas, wherein an output from a symmetric t-copula may bescaled using a corresponding marginal t-distribution and/or forecastedEWMA volatility.

In some cases, a Monte Carlo method may define a domain of possibleinputs such as correlation scenarios that may be generated by the riskfactor scenario generator 1125. In some cases, the salientcharacteristics of risk factors may include non-uniform autocorrelationsacross tenors and/or entities, heteroscedasticity, varying degrees ofheavy tails (e.g., observed, but having statistically weak symmetry),stable average correlations between single names, indices and between asingle name and an index. In some cases, the risk factors may havestrong correlation across tenors and/or strong dependence across anon-the run index and an off-the-run index of the same index family. Insome cases, a correlation may break down in a distressed market.Further, jumps, such as a default or a drastic improvement in creditquality may impact the calculations. In some cases, the different riskfactors may be interdependent where a movement in one risk factor may bereflected in a movement in another risk factor. As such, the spread riskfactor calculator 1120 may use one or more correlation matrices (e.g., ahigh correlation matrix, a low correlation matrix, a base correlationmatrix) to add countercyclicality to facilitate modeling of jointmovement of different risk factors.

In some cases, the risk factor scenario generator 1125 may generatescenarios that may be associated with one or more correlation matrices.For example, the risk factor scenario generator 1125 may generate one ormore scenarios that may reflect the different risk factors, such as tailparameter estimates, autocorrelation estimates, long-run autocorrelationestimates, EWMA volatility forecasts, and/or long-run volatilityestimates, and the like, such as those shown in FIG. 18. In some cases,the risk factor scenario generator 1125 may receive, at an input one ormore correlation scenarios, such as a historical correlation matrix, ahigh correlation matrix, and/or a low correlation matrix. In some cases,one or more of the historical correlation matrix, high correlationmatrix or low correlation matrix may be calculated internally by therisk factor scenario generator 1125. In some cases, the spread riskfactor calculator 1120 and/or the risk factor scenario generator maydetermine a historical VaR based on the historical correlation matrix, abasis VaR based on the low correlation matrix, and a systematic VaRbased on the high correlation matrix. The spread risk factor calculator1120 may then calculate a spread risk factor based on the historicalVaR, the basis VaR and the systematic VaR. For example, the spread riskfactor calculator 1120 may calculate the spread risk factor as a sum ofthe base spread risk factor (e.g., VaR_(Base)) and a maximum value ofeither a basis risk requirement (e.g., VaR_(Basis)−VaR_(Base)) or asystematic risk requirement (e.g., VaR_(Systematic)−VaR_(Base)). In somecases the determined maximum value may be multiplied by a scalar α,where α may be an integer or a fraction.

In some cases, the spread risk factor calculator 1120 may beconfigurable to determine the spread risk factor differently for margincalculations and stress evaluations. For example, the spread risk factorcalculator 1120 may be configured to receive an input (e.g., receivedvia a user interface screen displayed on the user interface 246)defining whether a margin calculation is being performed, such as by themargin calculator 1160, or whether a stress evaluation is beingperformed, such as by a stress evaluation module 1170. Based on thisinput, the stress evaluation module 1170 may determine a stress spreadrisk factor as a sum of the historical VaR, and a fraction of maximum ofeither the basis VaR or the systematic VaR, wherein a first quantile ofP&L distribution associated with a stress spread risk factor is greaterthan a second quantile of P&L distributions associated with a marginspread risk factor.

At 1220, the risk modeling computer system 1110 and/or the idiosyncraticrisk factor calculator 1130, may calculate an idiosyncratic risk factorcorresponding to a jump-to-default (JTD) charge and/or a jump-to-health(JTH) charge associated with the portfolio. In some cases, theidiosyncratic risk factor calculator 1130 may process instructions thatcause the idiosyncratic risk factor calculator 1130 to calculate anoverall portfolio VaR associated with the portfolio. In some cases, aJTD value-at-risk (VaR) associated with each single name positionassociated with the portfolio may be calculated. Each JTD VaR comprisesa default charge associated with a particular single name position and aremaining portfolio VaR corresponding to a remaining portion of theportfolio after removing the particular single name position. Further, amaximum JTD VaR of the JTD VaR associated with each single name positionmay also be calculated. The idiosyncratic risk factor calculator 1130may then calculate the JTD charge as a difference between the maximumJTD VaR and the overall portfolio VaR. Similarly, the idiosyncratic riskfactor calculator 1130 may calculate a JTH value-at-risk (VaR)associated with each single name position associated with the portfolio.For example, each JTH VaR comprises a default charge associated with aparticular single name position and a remaining portfolio VaRcorresponding to a remaining portion of the portfolio after removing theparticular single name position. A maximum JTH VaR of the JTD VaRassociated with each single name position may be calculated for use incalculation a JTH charge. The JTH charge may be calculated as adifference between the maximum JTH VaR and the overall portfolio VaR.

In some cases, the idiosyncratic risk factor calculator 1130 maycalculate the remaining portfolio VaR associated with the portfolioafter removing the particular single name position. In doing so, eachindex position in the remaining portion of the portfolio may be adjustedto account for the removal of the particular single name position.Further, the default charge associated with the particular single nameposition may be calculated as a difference between a current price ofthe particular single name position and a minimum recovery rate observedthrough a history associated with the particular single name position.

If the idiosyncratic risk factor calculator 1130 is calculating theidiosyncratic risk associated as part of a margin requirementcalculation associated with a CDS portfolio, the margin JTD chargeassociated with the portfolio may be calculated based on a historicalcorrelation scenario set, wherein the margin JTD charge is used incalculating a margin requirement associated with the portfolio. Themargin JTH charge associated with the portfolio based on a historicalcorrelation scenario set, wherein the margin JTH charge is used incalculating a margin requirement associated with the portfolio

In performing a stress calculation corresponding to the CDS portfolio,one or more different data sets may be used in calculating a stress JTDcharge. For example, a historical JTD charge may be calculated using ahistorical correlation scenario set, a basis JTD charge may becalculated using a basis correlation scenario set, a systematic JTDcharge may be calculated using a systematic correlation scenario set anda stress JTD charge associated with the portfolio may be calculated as amaximum of the historical JTD charge, the basis JTD charge and thesystematic JTD charge. In some cases, the stress JTD charge is used indetermining a stress requirement associated with the portfolio. A stressJTH charge associated with the portfolio may be calculated as a maximumof a historical JTD charge calculated using a historical correlationdata set, the basis JTD charge calculated using a basis correlation dataset and the systematic JTD charge calculated with a systematiccorrelation data set, wherein the stress JTD charge is used indetermining a stress requirement associated with the portfolio.

At 1230, the risk modeling computer system 1110 may calculate, such asby using the interest rate risk factor calculator 1150, an interest raterisk factor corresponding to losses associated with the portfolio due toa change in interest rates. In some cases, the interest rate risk factorcalculator 1150 may calculate an up-shock loss associated with an upshock to an interest rate curve used in CDS pricing and calculate adown-shock loss associated with a down shock to the interest rate curveused in CDS pricing. The interest rate risk factor calculator 1150 maythen calculate the interest rate risk factor as a maximum of theup-shock loss and the down-shock loss. In some cases, the size of theup-shock and a size of the down shock may be calibrated to a referencepivot rate.

At 1240, the risk modeling computer system 1110 may calculate, such asby using the liquidity risk factor calculator 1140, a liquidity riskfactor corresponding to a liquidity charge associated with theportfolio. In some cases, the liquidity risk factor calculator 1140 maybe configured to process instructions as described above in regards toFIG. 3. For example, the liquidity risk factor calculator 1140 (e.g.,the liquidity charge computing device 210) may be configured tocalculate an outright exposure to an investment grade (IG) sub-portfolioof the portfolio, calculate an outright exposure to a high yield (HY)sub-portfolio of the portfolio, calculate a basis exposure to at leastone of an index-based CDS sub-portfolio and a basis exposure to a singlename CDS sub-portfolio of the portfolio, and calculate the liquidityrisk factor based on the outright exposure of the IG sub-portfolio, theoutright exposure of the HY sub-portfolio and the basis exposure of theCDS portfolio.

In some cases, the liquidity risk factor may represent a requirementdesigned to capture the liquidity and concentration premium that aclearinghouse may have to pay during liquidation of the credit portfolioof a defaulted member. This premium may be proportional to the loss thatthe buyer anticipates to incur over the period required to unwind theportfolio. For large positions, this loss may scale super-linearly bythe number of days liquidation will take at a constant unwinding rateand, therefore, by the position size. There are theoretical and/orempirical justifications for appropriately selecting the position sizescaling exponent for liquidity charge at 1.5.

For a portfolio of credit instruments, the buyer may anticipate thecosts associated with hedging the outright exposure of sub portfolioswith the corresponding most liquid credit instruments. For example, forIG index and single name sub-portfolios, an IG OTR 5-year instrument maybe used. Similarly, for HY index and single name portfolios, a HY OTR5-year instrument may be used. The costs associated with liquidation ofthe hedged portfolio may depend on the liquidity profile of the basisposition (e.g., OTR/OTR-1 5-year versus OTR 5-year/OTR-10 10-year,etc.). The proposed liquidity requirement takes into account positionspecific liquidity characteristics such as spread volatility of theunderlying entity's most liquid tenor (e.g., loss during liquidation),weekly trading volume of the underlying name (e.g., concentration), andspread risk sensitivity of the underlying entity (SDV01).

In some cases, the liquidity charge computing device (e.g., theliquidity risk factor calculator 1140 of FIG. 11) may calculate theliquidity charge as a sum of different charges. In an illustrativeexample, the liquidity charge may be calculated as a sum of 4 charges,LC=(1)+(2)+(3)+(4). In this example, the first two terms of the equationmay equal

(1)+(2)=α_(1,IG)*abs(SDV _(1G))^(1.5)+α_(1,HY)*abs(SDV _(HY))^(1.5)

For example, element (1) may be the cost for hedging the IGsub-portfolio with an OTR IG 5Y index, where SDV1G may be the SDV01 ofthe IG sub-portfolio. In other words, the this first term may representa cost associated with IG indices and IG single names that are hedgedusing IG index Similarly, (2) may be the cost for hedging the HYsub-portfolio with an OTR HY 5Y index, where SDV_(HY) may be the SDV01of the HY sub-portfolio, In other words, this second term may berepresent a cost associated with HY indices and HY single names whichare hedged using HY index

After step (1) and (2), the portfolio may be considered to be SDV01neutral. At such time, the portfolio may be split into hedged “buckets”that will be liquidated with a speed dependent upon the trading volumeof the hedged instruments. For example, as the trading volume of theunderlying instrument increases, the liquidation speed may be increased.Similarly, as the trading volume of the underlying instrument decreases,the liquidation speed may be decreased.

$(3) = {\sum_{\underset{\underset{{- {HY}}\mspace{14mu} {OTR}\mspace{14mu} 5Y}{{- {IG}}\mspace{14mu} {OTR}\mspace{14mu} 5Y}}{i \in {IND}}}{a_{2}*{{{SDV}\; 01_{0i}}}*{vol}_{i}*\max \left\{ {\left( \frac{Q_{i}}{Q_{0i}} \right)^{1.5},\frac{Q_{i}}{Q_{0i}}} \right\}}}$

In (3), Q_(0i) is the run rank based median trading volume over theprevious 3 months, SDV01^(0i) is the SDV01 of the index i computed for anotional equal to Q_(0, and) Vol_(i) is the log-return volatility of5-year index i. Further, the risk related to each position index i, maybe represented by the product of the SDV01 and the volatility and theliquidity of each index position i may be represented by the tradingmedian volume Q_(0i). In some cases, the IG and HY OTR 5Y may not beincluded in the calculation. Rather, these indices may be used as hedgesand liquidated as a roll. If Qi<Q0i, then the entire position may beliquidated very quickly (e.g., linear scaling with the notional).However, if Q_(i)>Q_(0i), then an exponent of 1.5 is applied torepresent an increase in the liquidation cost due to the size of Q_(i)(e.g., a super linear scaling with notional).

$(4) = {\sum_{\underset{\underset{{- {HY}}\mspace{14mu} {OTR}\mspace{11mu} 5Y}{{- {IG}}\mspace{14mu} {OTR}\mspace{14mu} 5Y}}{i \in {SN}}}{a_{3}*{{{SDV}\; 01_{0i}}}*{vol}_{i}*\max \left\{ {\left( \frac{Q_{i}}{Q_{0i}} \right)^{1.5},\frac{Q_{i}}{Q_{0i}}} \right\}}}$

As can be seen, (4) may be similar to (3), but used for single namepositions rather than indices. Q_(0i) is the median trading volume ofsingle name i over the previous 3 months, SDV01_(0i) is the SDV01 of thesingle name i computed for a notional equal to Q₀, and Vol_(i) is thelog-return volatility of 5-year single name i.

At 1250, the risk modeling computer system 1110 may calculate, such asby using the margin calculator 1160, a margin requirement for theportfolio based, at least in part on the spread risk factor, theidiosyncratic risk factor, the interest rate risk factor, and theliquidity risk factor. In some cases, the risk modeling computer system1110 may perform one or more stress evaluations on the portfolio andcalculate a stress requirement associated with the portfolio based, atleast in part on the spread risk factor, the idiosyncratic risk factor,the interest rate risk factor, and the liquidity risk factor.

FIG. 13 shows a flow chart illustrative of a risk factor calibrationsystem 1300 for use in generating a risk model according to at leastsome embodiments. For example, the risk factor calibration system may beincorporated into one or more portions of the clearing house computingsystem 240, including the risk modeling computing system 1110 and/or thespread risk factor calculator. The risk factor calibration system 1300may process instructions to calibrate one or more raw risk factors, suchas daily log changes in par-spreads for entity and tenor. For example,the risk factor calibration may include an autocorrelation estimationthat may include historical volatility estimation of de-autocorrelatedrisk factors, such as exponential weighted moving average (EWMA) with adecay factor, λ. The historical risk factors used in these calculationsmay be obtained from a data repository containing historical marketinformation. The historical risk factors may be obtained for a specifiedtime period (e.g., t_(h)−t). In some cases, t may be any arbitrarilychooses date or may be at or near a present date (e.g., within a day,week or month). The risk factors, EWMA volatility parameters, and/or theautocorrelation data may be used in a residual estimation calculation.For example, residual estimation may be performed usingde-autocorrelated and/or standardized risk factors (residuals). Theresiduals for the historical time period may then be used for anestimation of student-t parameters and an estimation of raw factorcorrelations (e.g., a historical correlation matrix). The raw historicalcorrelation matrix may then be cleaned using one or more methods, suchas principal component analysis (PCA) and/or Random Matrix Theory (RMT)to generate a clean historical correlation matrix.

Risk factors may be obtained over a specified time period, such as froma specified historical time (e.g., t−H) to a present time (e.g., t). Forexample, historical risk factors may be defined as risk factors obtainedfrom a time period between 2008 and 2013. These historical risk factorsmay be sued to generate a series of EWMA volatility parameters and/or aseries of autocorrelations. These parameters, historical values andautocorrelations may then be used to determine residuals for thehistorical time period. These residuals may then be used to generate aparameter set (e.g., a student-t tail parameter set) and a historicalcorrelation matrix containing raw data. This correlation matrix then maybe modified (e.g., cleaned) using one or more different methods, such asPCA or RMT.

Estimation of risk factor distribution may be determined for a giventenor τ and name I, by processing instructions by a computing device 244of the clearinghouse computing system 240. In some cases, the name i maycorrespond to one of a name of an index CDS or a name of a single nameCDS. For a given tenor and name:

R _(i,τ)(t)=a _(i,τ)(t)R _(i,τ)(t−1)+σ_(i,τ)(t)ε_(i,τ)  (a)

where R_(i)(k, t) is a daily log-return of the risk factor par spreads,

R _(i,τ)(t)=ln CDS _(i,τ)(t)−ln CDS _(i,τ)(t−1)  (b)

a_(i,τ)(t) is an autoregressive AR(1) coefficient for theautocorrelation observed in R_(i,τ)(t):

a _(i,τ)(t)=1/756Σ_(s=1) ⁷⁵⁶ Ri,τ(t−s+1)*Ri,τ(t−s)

and σ_(i,τ)(t) is a volatility scale factor defined as the EWMA standarddeviation of the residuals of AR(1) model:

${\sigma_{i,\tau}(t)} = {\frac{1}{\sum\limits_{s = 1}^{252}\lambda^{s - 1}}{\sum\limits_{s = 1}^{252}{\lambda^{s - 1}\left\lbrack {X_{i,\tau}\left( {t - 2} \right)} \right\rbrack}^{2}}}$

where X_(i,τ)(t) is the de-autocorrelated daily log-return

X _(i,τ)(t)=R _(i,τ)(t)−a _(i,τ)(t)R _(i,τ)(t−1)

Calibration of countercyclical parameters may include σ _(i,τ)(t), whichis a long-run volatility component which introduces contercyclicality inindividual risk factor variations:

${{\overset{\_}{\sigma}}_{i,\tau}(t)} = {\frac{1}{{N_{i,\tau}(t)} - 1}{\sum\limits_{s = 0}^{{N_{i,\tau}{(t)}} - 1}{R_{i,\tau}\left( {t - s} \right)}^{2}}}$${{\overset{\_}{a}}_{i,\tau}(t)} = {\frac{1}{N_{i,\tau} - 1}{\sum\limits_{s = 1}^{N_{i,\tau} - 1}{{R_{i,\tau}\left( {t - s + 1} \right)}*{R_{i,\tau}\left( {t - s} \right)}}}}$

is a long-run autocorrelation estimate which introducescountercyclicality for scaling daily volatility to margin period of risk

C^(low) and C^(high) are two correlation matrices which addcountercyclicality to modeling of the joint movement of risk factors,where

$C^{low} = {{\begin{pmatrix}1 & 0 & 0 & 0 & 0 & 0 \\0 & \ddots & \ddots & \ddots & \ddots & \ddots \\0 & \ddots & 1 & \ddots & \ddots & \ddots \\0 & \ddots & \ddots & 1 & {\overset{\_}{\rho}}_{I,I} & {\overset{\_}{\rho}}_{I,I} \\0 & \ddots & \ddots & {\overset{\_}{\rho}}_{I,I} & \ddots & \ddots \\0 & \ddots & \ddots & {\overset{\_}{\rho}}_{I,I} & \ddots & 1\end{pmatrix}\mspace{14mu} {and}\mspace{14mu} C^{high}} = \begin{pmatrix}1 & 1 & 1 & 1 & 1 \\1 & \ddots & \ddots & \ddots & \ddots \\1 & \ddots & \ddots & \ddots & \ddots \\1 & \ddots & \ddots & \ddots & \ddots \\1 & \ddots & \ddots & \ddots & \ddots\end{pmatrix}}$

In some cases, as part of the scenario generation, a Monte Carlosimulation may be run. For example, for each Monte Carlo simulation,j=1, . . . , N_(MC), the spread shock to a given tenor τ of name I(e.g., a single name, an index, etc.) may be given by:

${R_{i,\tau}^{(j)}\left( {t + n} \right)} = {\left\lbrack {{{\hat{\sigma}}_{i,\tau}\left( {t + 1} \right)}\bigvee{{\hat{\sigma}}_{i,\tau}\left( {t + 1} \right)}} \right\rbrack \sqrt{n + {2\left( {n - 1} \right)\left( {{a_{i,\tau}(t)}\bigvee{{\overset{\_}{a}}_{i,\tau}(t)}\bigvee 0} \right.}}\xi_{i,\tau}^{(j)}}$  where$\mspace{20mu} {{{{\left. \xi_{i,\tau}^{(j)} \right.\sim\sqrt{\frac{{\hat{v}}_{i,\tau} - 2}{{\hat{v}}_{i,\tau}}}}t_{{\hat{v}}_{i,\tau}}} - {1\left( {{Rank}\left\lbrack z_{i,\tau}^{(j)} \right\rbrack} \right)}},{where}}$  z_(i, τ)^((j)) ∼ t_(v_(c))() − 1(Rank[z_(i, τ)^((j))]), where

z_(i,τ) ^((j))˜t_(v) _(c) (

) is a simulated multivariate Student-t variable with correlation matrix

and a common degree of freedom of t_(v) _(c)

σ _(i,τ)(t+1) is the EWMA volatility forecast at margin/stress date t,where, for margin calculations σ _(i,τ)(t+1)=σ_(i,τ)(t+1) and for stresscalculations σ _(i,τ)(t+1) is the larger of 99.75% percentile of{σ_(i,τ)(s+1)}_(s≤t) and a constant multiple of σ_(i,τ)(t+1) where theconstant is calibrated to a cross section of risk factors during aparticular year (e.g., 2008, 2009, etc.).

is set to

₀(t),

^(low) and

^(high) for base, basis and systematic margin requirement calculations,respectively. Further, in some cases, v_(c) and N_(MC) may be constants(e.g., v_(c)=3 and N_(MC)=10,000, etc.).

Idiosyncratic Risk Requirement

Idiosyncratic risk requirement may be the sum of a Jump-to-Default (JTD)and a Jump-to-Health (JTH) charge. These charges may be add-on riskcharges to cover for the default and drastic improvement in creditquality of single names. A calculation of JTD charge may start withremoving each single name CDS one at a time from the portfolio. VaR ofthe remaining portfolio may be calculated after adjusting each indexposition notional to account for the removal of the single name (reducenotional by a ratio of one over the number of constituents). The defaultcharge for the removed entity may be calculated as the differencebetween current price and the minimum recovery rate observed through thehistory of the single name entity. The default charge may be added tothe VaR of the remaining portfolio. This calculation may be repeated foreach single name that the portfolio has explicit (single name position)or implicit (constituent in an index position) exposure to. The maximummay be taken over all single names to calculate the JTD VaR of theportfolio. The difference between the JTD VaR and the original VaR maybe the JTD charge. For margin purposes, this calculation may be doneonly for the historical correlation scenario set. For stresscalculations, the same process may be repeated for historical, low andhigh correlation scenario sets and the maximum charge may be chosen asthe JTD risk requirement.

A calculation of a JTH charge is very similar to that of JTD. One majordifference is that there is no JTH charge for pure index portfolios.This may be based on an analysis of index spread changes or index spreadbasis changes on days when a constituent experiences a drasticimprovement in credit quality. For portfolios with single namepositions, each single name may be removed from the portfolio one at atime. The remaining portfolio VaR may be calculated and a JTH charge isadded to it. The JTH charge may be the difference between the currentprice of the position and the price of the position in an extremequantile scenario from the high correlation scenario set. The selectionof the scenario from the high correlation scenario set allows us tomodel the effect of credit improvement across all tenors of the sameunderlying. The JTH VaR which may be the sum of the remaining portfolioVaR and the JTH charge may be computed for each single name entity andthe maximum is taken. The difference between the original VaR and themaximum JTH VaR may be the JTH risk requirement. The same distinctionbetween margin and stress JTD may apply to JTH calculations, as well.

In some cases, the idiosyncratic risk factor calculator 1130 may use JTHand JTD risk requirements as add-on risk charges to cover for thedefault and/or drastic improvement in credit quality of an entity (e.g.,a single name). Credit entities may be removed one at a time from theportfolio. Base spread requirements of the remaining portfolio isrecalculated. For JTD, index position scenario P&L's are reduced by aratio of 1/(number of index constituents). For JTH, index positionscenario P&L's are not adjusted. Each spread scenario P&L is added a JTDand JTH P&L for the removed entity. For JTD, (total single name notionalwith index decomposition)*(RR-current price). For JTH, (Single namenotional)*(price at low percentile (0.5%) spread of high correlationscenarios—Current price). JTD and JTH quantiles are calculated from thenew scenario P&L's for each entity k, using VaR_(P) ^(idio,k). The finalJTD and JTH risk requirements are calculated as max_(k){VaR_(P)^(JTD,k)−VaR_(P) and max_(k){VaR_(P) ^(JTH,k)}−VaR_(P), respectively.

Interest Rate Risk Requirement

FIG. 19 shows an illustrative method 1900 for determining an interestrate sensitivity charge according to at least some embodiments. Aninterest rate risk requirement, such as the interest rate sensitivitycharge, may be intended to cover losses in credit portfolios due toextreme moves in interest rates. The charge may be computed as themaximum of the losses under parallel up and down shocks to the interestrate curve used for CDS pricing. The shock sizes may be calibrated to areference pivot rate.

For example, the illustrative method may be processed as instructions bythe interest rate risk factor calculator 1150 to calculate the interestrate sensitivity factor. In some cases, the interest rate sensitivitycharge may be used to cover losses due to changes in interest rate termstructures. The sensitivity is mainly due to the parallel upward anddownward shifts of the interest rate (IR) curve. In an illustrativeexample, at 1910, a log-return history of the 5-year rate may bedetermined from the IR curve. Using the log-return history, an up shock(e.g., a 99% quantile, a 99.5% quantile, etc.) may be determined at 1920and a down shock (e.g., a 1% quantile, a 0.5% quantile, etc.) may bedetermined at 1930. Using the up shock and the down shock, the interestrate sensitivity module may determine an “up-scenario” IR curve at 1940and a “down-scenario” IR curve at 1950. From the up-scenario IR curve,the interest rate risk factor calculator 1150 may determine one or moreP&L scenarios, such as the one or more P&L up scenarios at 1960 and theone or more P&L down scenarios at 1970. From these P&L up scenarios andthe P&L down scenarios, the interest rate risk factor calculator 1150may determine, at 1980, an interest rate sensitivity charge based on aminimum of the P&L up and P&L down scenarios using the equation: (IRScharge)=−min{P&L_(up), P&L_(down)}.

Spread Risk Requirement

A Monte Carlo based scenario generation approach may be used to samplerisk factor scenarios that are in line with the salient characteristicsof the index and single name log spread changes.

Given the risk factor scenarios under historical, low and highcorrelation scenario sets, the overall spread risk requirement may becalculated as a combination of value at risk (VaR) numbers under each ofthe correlation setups. For margin, the spread risk requirement may bethe sum of the historical VaR and a fraction of the maximum of lowcorrelation scenario set VaR (e.g., Basis VaR) and the high correlationscenario set VaR (e.g., Systematic VaR). The fraction may be calibratedto backtesting results for margin calculations and may be set to one forstress calculations. The stress VaR may be computed from a higherquantile of scenario P&L distribution compared to margin VaR. In anexample, FIG. 17 shows an illustrative backtesting framework for testinga risk model for a CDS portfolio according to at least some embodiments.The backtesting framework may be used to test directional risk, andexposure based on DV01 and/or SDV01. In some cases, the models may bebacktested using targeted portfolios 1700 and/or diversified portfolios1750 that may include representations of different strategies includecurve, pair, roll, pair×curve, index arbitrage, basis, sector,basis×sector, and sector×curve strategies. FIGS. 23-24 show illustrativebacktesting results based on historical portfolio information using therisk modelling techniques according to at least some embodiments.

FIGS. 14 and 15 show an illustrative method for determining a totalspread risk requirement for a risk model of a CDS portfolio according toat least some embodiments. For example, FIG. 14 shows an illustrativeprocess that may use a Monte Carlo based approach to determine the totalspread risk requirement for the CDS portfolio. For example, the MonteCarlo based scenario generation approach may be used to sample riskfactor scenarios that are in line with the salient characteristics ofthe index and single name log spread changes. For example, thedependence across different risk factors may be modeled to showinterdependence of variables, such as by using a copula. In an example,a symmetric copula (e.g., a student t-copula, a Gaussian copula, etc.)with multiple degrees of freedom may be used, such as a symmetrict-copula having 4 degrees of freedom may be used. Statistical tests maybe performed on the empirical copula for pairs of risk factors tojustify the choice of the multivariate copula distribution. Symmetricnature of the dependence structure may also be tested.

Three different correlation scenarios may be input to the risk factorscenario generator (e.g., a copula Monte Carlo scenario generator) toestimate a base, basis and systematic Value-at-Risk (VaR), including ahistorical correlation matrix, a high correlation matrix and a lowcorrelation matrix. The historical correlation matrix may comprise a rawhistorical correlation matrix that may be a sample correlation matrix ofempirical residual ranks. This raw historical correlation matrix may becleaned for removing spurious correlations and noise using one or moredifferent methods, such as random matrix theory (RMT) and principalcomponent analysis (PCA) methods. The high correlation matrix may be acounter cyclical correlation matrix that may imply perfect positivecorrelation among all risk factors which leads to Systematic VaR. Thelow correlation matrix may be a counter cyclical correlation matrix thatmay imply zero correlation among all risk factors, except for index toindex pairs, which leads to Basis VaR

The risk factor scenarios output from a t-copula as computed by the riskfactor scenario generator may be scaled by their corresponding marginalt-distributions and the forecasted exponential weighted moving average(EWMA) volatilities. The scaling with EWMA volatilities may also takeinto account scaling from 1-day shocks to margin period-of-risk shocks(5-day). This may be done by taking into account the first order effectof autocorrelations.

The marginal distribution of each risk factor may be calibrated to itsown time-series. This allows differentiating between the extents ofheavy-tailed behavior across different risk factors. Each risk factormay be assumed to have a Student t-distribution. The degree of freedommay be determined by Anderson-Darling test. An empirical analysis on thesymmetric nature of the residual distribution may be used to justify thechoice of symmetric t-distribution. The fitted t-distribution may beused to transform empirical residuals to residual ranks.

The t-distribution for each risk factor may be fitted to the time-seriesof empirical residuals. Empirical residuals are simply de-autocorrelatedand standardized log changes of risk factors. This standardization maybe done using EWMA estimates of volatility.

For stress calculations, the volatility scalar may be taken as themaximum of a multiple of the EWMA forecast and the maximum of thehistorical EWMA forecasts. The multiplier for the current EWM forecastmay be calibrated to the results of a cross sectional analysis ofpost/pre Lehman EWMA forecasts across different risk factors.

As shown in FIG. 15, given the risk factor scenarios under historical,low and high correlation scenario sets, the overall spread riskrequirement may be calculated as a combination of VaR numbers under eachof the correlation setups. For margin, the spread risk requirement maybe the sum of the historical VaR and a fraction of the maximum of lowcorrelation scenario set VaR (Basis VaR) and the high correlationscenario set VaR (Systematic VaR). The fraction may be calibrated tobacktesting results for margin calculations and may be set to one forstress calculations. The stress VaR may be computed from a higherquantile of scenario profit and loss (P&L) distribution as compared tomargin VaR. The total spread risk requirement may be calculated usingthe formula: total spread risk requirement (TSRR)=Base spread riskrequirement+α max{basis risk requirement, Systematic risk requirement}.

TSRR=(VaR_(P)base)+αmax{(VaR_(P)basis−VaR_(P)base),(VaR_(P)systematic−VaR_(P)base)}

Stress Model

For determining a size of a guaranteed fund, a stress model may be used.In some cases, the stress model may be an extension of the margin model.As shown in FIG. 16, the stress spread risk requirement may becalculated from a higher quantile of the P&L distribution acrossscenarios, for example VaR_(q) may represent the stress spread riskrequirement (e.g., value at risk), where q=99.75%. The number ofentities considered for JTD using the stress model may be limited to apreselected number, such as by selecting a constant number (e.g., 2).The JTH spread may be computed from a lower percentile of the highcorrelation scenarios (e.g., 0.05%), where the spread risk requirementmay be the maximum of base, basis and systematic stress VaR (e.g.,αStress=1). The stress volatility forecast may be chosen as the maximumof 99.75% of the historical EWMA volatility or 2.35 times the mostrecent EWMA volatility. The interest rate risk requirement may becomputed from 0.25% and 99.75% percentiles of historical log changes ofthe 5 year point on the IR curve.

The stress model may be used for determining a size of a guarantee fundassociated with a cleared credit portfolio. The stress model may be anextension of the margin model, where the stress spread risk requirementmay be calculated from a higher percentile of the P&L distributionacross scenarios (e.g., VaR_(q), where q=99.75%). In the calculation, anumber of entities may be considered for the jump-to-default. Forexample, two entities may be considered in the jump-to-defaultcalculations. Similarly, the JTH spread may be computed from a lower(e.g., 0.05%) percentile of the high correlation scenarios. The spreadrisk requirement is the maximum of the base, basis and system stressVaR, where α_(stress)=1. Further, the stress volatility forecast may bechosen to be the maximum of the (99.75% percentile of historical EWMAvolatility) and (2.3 times the most recent EWMA volatility). In somecases, the interest rate risk requirement may be computed from the 0.25%and the 99.75% percentile of historical log changes of the 5-year pointon the IR curve.

The stress model of the RMCC, as implemented using the clearinghousecomputing system 240, may allow for a comprehensive set of scenarios.Parameter sets used with the stress model may be used to cover “extremebut plausible scenarios.” For example, these scenarios may be used toaddress low probability, but high impact risk factors resulting fromcertain situations. By combining the margin model and the stress modelin the RMCC, use of both the margin model and the stress model may besimple and intuitive and results may be easy to replicate by end users.

The risk model may be used to analyze and/or model statistical featuresof credit spread movements for one or both of single name CDS and CDSindices. For example, the RMCC may allow for time series analysis ofdifferent risk factors (e.g., spread log changes, etc.) associated witha particular CDS product and/or with a portfolio of CDS products. Forsingle name CDS products, the risk factors may include par spreads atfixed benchmark tenors (e.g., 1 year, 3 year, 5 year, 7 year, 10 year,etc.). For CDS indices, the risk factors may include par spreads ofsynthetic on the run or off the run (OTR) indices (e.g., OTR_(−k) (k=0,1, . . . ) at a fixed maturity) that may be interpolated at fixedbenchmark tenors to preserve stationarity. For the RMCC, salientcharacteristics of risk factors may include autocorrelations that may benon-uniform across entities and tenors, heteroscedasticity, varyingdegrees of heavy tails that may be observed but have statistically weakasymmetry, stable average correlations (e.g., Single name-Single name,Single name-Index, Index-Index, and the like). In some cases, thecharacteristics may have strong correlations across tenors, strongdependence across on-the-run and off-the-run indices of the same indexfamily, an index on a constituent basis, a breakdown of correlations indistressed markets and or jumps which may be defaults (jump-to-default)and/or drastic improvements (e.g., a jump to health) in credit quality.

In some cases, the RMCC may be modeled using a risk modeling computingsystem that may be associated with a financial institution and/or aclearinghouse. The risk modeling computing system may be configured tostore models in a data repository and/or another non-transitory memorydevice as instructions and/or other information (e.g., parameters, CDSmarket information, CDS index information, CDS single name information,and/or the like. For example, the risk modeling computing system mayinclude one or more computing devices configured to retrieve theinstructions and/or other information from the data repository and/ornon-transitory memory device via a network to generate a risk model foruse as the RMCC by a risk model generator. In some cases, the risk modelgenerator may design the RMCC using one or more different model types,such as a factor model or a scenario based model. Each model hasassociated advantages and disadvantages. For example, factor models maybe simple and easy to calibrate, but may provide incoherent modeling ofportfolio benefits. For example, the factor model may include rule basedcorrelation offsets. However, these offsets may not be readilyextendible to new risk factors which may be introduced to the model overtime. Factor based models also may rely on a decomposition model forefficiency, for both basis and curve decomposition, but may be prone todouble counting of risk associated with the portfolio.

Scenario based models may be considered to be comprehensive models dueto explicit correlation modeling performed as part of the scenario basedmodel. As such, scenario based models may be more easily extended to newrisk factors. Due to availability of historical data, the scenario basedmodels (e.g., a historical model, a Monte Carlo model, etc.) may need tobe implemented parsimoniously. Further, scenario based models may bemore complex than other model types and, as such, may be more difficultto calibrate. However, scenario-based models may offer greater stabilityof modeling parameters through the use of correlations anddistributions.

Results

FIGS. 20-22 show charts illustrative of a margin impact based on therisk model for a CDS portfolio according to at least some embodimentsand FIGS. 23-24 show illustrative backtesting results of historicalportfolio information based on the risk model according to at least someembodiments. FIG. 20 illustrates the resulting impact on margin accountsacross clearing member firms associated with the clearing house. As canbe seen, the margin requirements may be recalculated on a periodic orintermittent basis. In the example of FIG. 20 the clearinghousecalculates margin requirements for cleared credit portfolios on amonthly basis (at the first of the month). Using historical data betweenNovember 2012 and October 2013, the margin requirements associated withcleared credit portfolios associated with clearinghouse members wererecalculated and totaled across the clearing member firms for eachmonth. Each monthly total was then compared to the previously calculatedmargin account totals determined using a previous model. In theillustrated example, the previously used model did not considerliquidity of the accounts in the margin determination. As can be seen.the margin requirements can be reduced, in some cases significantly, byusing the model discussed above. FIG. 24 illustrates a margindetermination associated with particular CDS portfolio types, such asthose using specified strategies. Here, the margin requirements havebeen broken down so that the margin requirement associated with ajump-to-default factor, a jump-to-health factor, an interest rate riskfactor, and a spread risk factor can be observed. As can be seen, ofthese listed factors, the spread risk factor has a greater impact thanthe other risk factors combined, excluding liquidity. FIG. 22 showsanother comparison between margin account/guarantee fund sizing acrossclearing member firms, where the margin account/guarantee fund sizes maybe determined using previously existent models and a model correspondingto the embodiments discussed herein. As can be seen, across thedifferent clearing member firms, the proposed size of the guaranteefunds can be reduced by approximately 20% (e.g., from about $150 millionto about $120 million). Further, in most cases, a proposed stress tomargin ratio can be reduced across most clearing member firms based onuse of the models discussed herein. FIG. 23 shows illustrative forwardbacktesting results performed on approximately 7000 portfolios usinghistorical data from between January 2010 and November 2013. In thiscase, the portfolios included both targeted and diversified portfolios.FIG. 24 shows illustrative backtesting results for the same portfolios,where the backtesting results included reverse backtesting usinghistorical information from January 2010 to January 2008, and forwardbacktesting using historical information from between January 2010 andNovember 2013. FIG. 25 shows illustrative charts displaying a marginbreak percentage of gross notional per a number of occurrences and aspread risk requirement break percentage of gross notional per a numberof occurrences.

The present invention has been described in terms of preferred andexemplary embodiments thereof. Numerous other embodiments, modificationsand variations within the scope and spirit of the invention will occurto persons of ordinary skill in the art from a review of thisdisclosure. For example, aspects of the invention may be used to processand communicate data other than market data.

1. (canceled)
 2. A credit default swap (CDS) risk modeling computingsystem comprising: a data repository storing a risk model for clearedcredit (RMCC), the RMCC being reactive to current market conditions andpersistent to extreme events and including both a margin model and astress model, the stress model being an extension of the margin model;at least one processor; and one or more non-transitory memory devicescommunicatively coupled to the at least one processor, thenon-transitory memory devices storing instructions that, when executedby the at least one processor, cause the CDS risk modeling computingsystem to: calculate, using a spread risk factor calculator, a spreadrisk factor, the spread risk factor corresponding to a value at risk(VaR) associated with a plurality of correlation scenario sets, whereinthe correlation scenario sets correspond to characteristics of at leastone of a single name credit default swap or an index credit default swapof the portfolio; calculate, using an idiosyncratic risk factorcalculator, an idiosyncratic risk factor corresponding to ajump-to-default (JTD) charge and a jump-to-health (JTH) chargeassociated with the portfolio; calculate, using an interest rate riskfactor calculator, an interest rate risk factor corresponding to lossesassociated with the portfolio due to a change in interest rates, whereinthe interest rate risk factor corresponds to at least an upshot loss anda down shock loss; calculate, using a liquidity risk factor calculator,a liquidity risk factor corresponding to a liquidity charge associatedwith the portfolio; calculate a margin requirement or a stressrequirement for the portfolio based, at least in part on the spread riskfactor, the idiosyncratic risk factor, the interest rate risk factor,and the liquidity risk factor using the margin model or the stressmodel, respectively; and present information corresponding to thecalculated stress requirement or the calculated margin requirement. 3.The CDS risk modeling computing system of claim 2, wherein the one ormore non-transitory memory devices further store instructions that, whenexecuted by the at least one processor, cause the spread risk factorcalculator to: model, using a Monte Carlo-based scenario generator, aplurality of risk factors using a symmetric t-copula with four degreesof freedom, wherein an empirical copula associated with risk factorpairs is used to justify a choice of a multivariate copula distribution.4. The CDS risk modeling computing system of claim 3, wherein the one ormore non-transitory memory devices further store instructions that, whenexecuted by the at least one processor, cause the scenario generator toreceive, at an input to the scenario generator, one or more correlationscenarios comprising a historical correlation matrix, a systemiccorrelation matrix, and a basis correlation matrix; and estimate one ormore of a base value-at-risk (VaR), a basis VaR, and a systematic VaRbased on the one or more correlation scenarios.
 5. The CDS risk modelingcomputing system of claim 4, wherein the one or more non-transitorymemory devices further store instructions that, when executed by the atleast one processor, cause the scenario generator to calculate a marginspread risk factor as a sum of the base VaR and a fraction of a maximumof either the basis VaR and the systematic VaR.
 6. The CDS risk modelingcomputing system of claim 4, wherein the one or more non-transitorymemory devices further store instructions that, when executed by the atleast one processor, cause the scenario generator to calculate a stressspread risk factor as a sum of the base VaR and a fraction of a maximumof either the basis VaR and the systematic VaR, wherein a first quantileof profit and loss (P&L) distributions associated with a stress spreadrisk factor is greater than a second quantile of P&L distributionsassociated with a margin spread risk factor.
 7. The CDS risk modelingcomputing system of claim 3, wherein the one or more non-transitorymemory devices further store instructions that, when executed by the atleast one processor, cause the scenario generator to: scale outputs fromthe symmetric t-copula by a corresponding marginal t-distribution and aforecasted exponential weighted moving average (EWMA) volatility.
 8. TheCDS risk modeling computing system of claim 7, wherein the one or morenon-transitory memory devices further store instructions that, whenexecuted by the at least one processor, cause the scenario generator toscale an EWMA volatility using a 1-day shock value and a marginperiod-of-risk shock value.
 9. The CDS risk modeling computing system ofclaim 8, wherein a multiplier for a EWMA forecast is calibrated to aresult of a cross sectional analysis of post or pre Lehman EWMAforecasts across different risk factors.
 10. The CDS risk modelingcomputing system of claim 2, wherein the one or more non-transitorymemory devices further store instructions that, when executed by the atleast one processor, cause the idiosyncratic risk factor calculator to:calculate an overall portfolio VaR associated with the portfolio;calculate a JTD value-at-risk (VaR) associated with each single nameposition associated with the portfolio, wherein each JTD VaR comprises adefault charge associated with a particular single name position and aremaining portfolio VaR corresponding to a remaining portion of theportfolio after removing the particular single name position; calculatea maximum JTD VaR of the JTD VaR associated with each single nameposition; and calculate the JTD charge as a difference between themaximum JTD VaR and the overall portfolio VaR.
 11. The CDS risk modelingcomputing system of claim 10, wherein the one or more non-transitorymemory devices further store instructions that, when executed by the atleast one processor, cause the idiosyncratic risk factor calculator to:calculate the remaining portfolio VaR associated with the portfolioafter removing the particular single name position, wherein each indexposition in the remaining portion of the portfolio is adjusted toaccount for the removal of the particular single name position; andcalculate the default charge associated with the particular single nameposition as a difference between a current price of the particularsingle name position and a minimum recovery rate observed through ahistory associated with the particular single name position.
 12. The CDSrisk modeling computing system of claim 10, wherein, the one or morenon-transitory memory devices further store instructions that, whenexecuted by the at least one processor, cause the idiosyncratic riskfactor calculator to: calculate a margin JTD charge associated with theportfolio based on a historical correlation scenario set, wherein themargin JTD charge is used in calculating a margin requirement associatedwith the portfolio.
 13. The CDS risk modeling computing system of claim10, wherein, the one or more non-transitory memory devices further storeinstructions that, when executed by the at least one processor, causethe idiosyncratic risk factor calculator to: calculate a historical JTDcharge using a historical correlation scenario set; calculate a basisJTD charge using a basis correlation scenario set; calculate asystematic JTD charge using a systematic correlation scenario set; andcalculate a stress JTD charge associated with the portfolio as a maximumof the historical JTD charge, the basis JTD charge and the systematicJTD charge, wherein the stress JTD charge is used in determining astress requirement associated with the portfolio.
 14. The CDS riskmodeling computing system of claim 2, wherein the one or morenon-transitory memory devices further store instructions that, whenexecuted by the at least one processor, cause the idiosyncratic riskfactor calculator to: calculate an overall portfolio VaR associated withthe portfolio; calculate a JTH value-at-risk (VaR) associated with eachsingle name position associated with the portfolio, wherein each JTH VaRcomprises a default charge associated with a particular single nameposition and a remaining portfolio VaR corresponding to a remainingportion of the portfolio after removing the particular single nameposition; calculate a maximum JTH VaR of the JTH VaR associated witheach single name position; and calculate the JTH charge as a differencebetween the maximum JTH VaR and the overall portfolio VaR.
 15. The CDSrisk modeling computing system of claim 14, wherein, the one or morenon-transitory memory devices further store instructions that, whenexecuted by the at least one processor, cause the idiosyncratic riskfactor calculator to: calculate a margin JTH charge associated with theportfolio based on a historical correlation scenario set, wherein themargin JTH charge is used in calculating a margin requirement associatedwith the portfolio; and calculate a stress JTH charge associated withthe portfolio as a maximum of a historical JTD charge calculated using ahistorical correlation data set, a basis JTD charge calculated using abasis correlation data set and a systematic JTD charge calculated with asystematic correlation data set, wherein the stress JTD charge is usedin determining a stress requirement associated with the portfolio. 16.The CDS risk modeling computing system of claim 2, wherein the one ormore non-transitory memory devices further store instructions that, whenexecuted by the at least one processor, cause the interest rate riskfactor calculator to: calculate an up-shock loss associated with an upshock to an interest rate curve used in CDS pricing; calculate adown-shock loss associated with a down shock to the interest rate curveused in CDS pricing; and calculate the interest rate risk factor as amaximum of the up-shock loss and the down-shock loss.
 17. The CDS riskmodeling computing system of claim 16, wherein a size of the up-shockand a size of the down shock are calibrated to a reference pivot rate.18. The CDS risk modeling computing system of claim 2, wherein the oneor more non-transitory memory devices further store instructions that,when executed by the at least one processor, cause the liquidity riskfactor calculator to: calculate an outright exposure to an investmentgrade (IG) sub-portfolio of the portfolio; calculate an outrightexposure to a high yield (HY) sub-portfolio of the portfolio; calculatea basis exposure to at least one of an index-based CDS sub-portfolio anda basis exposure to a single name CDS sub-portfolio of the portfolio;and calculate the liquidity risk factor based on the outright exposureof the IG sub-portfolio, the outright exposure of the HY sub-portfolioand the basis exposure of the CDS portfolio.
 19. A method of modelingcredit default swap (CDS) risk, the method comprising: retrieving, by atleast one processor, a risk model for cleared credit (RMCC), the RMCCbeing reactive to current market conditions and persistent to extremeevents and including both a margin model and a stress model, the stressmodel being an extension of the margin model; calculating, by the leastone processor, a spread risk factor, the spread risk factorcorresponding to a value at risk (VaR) associated with a plurality ofcorrelation scenario sets, wherein the correlation scenario setscorrespond to characteristics of at least one of a single name creditdefault swap or an index credit default swap of the portfolio;calculating, by the least one processor, an idiosyncratic risk factorcorresponding to a jump-to-default (JTD) charge and a jump-to-health(JTH) charge associated with the portfolio; calculating, by the leastone processor, an interest rate risk factor corresponding to lossesassociated with the portfolio due to a change in interest rates, whereinthe interest rate risk factor corresponds to at least an upshot loss anda down shock loss; calculating, by the least one processor, a liquidityrisk factor corresponding to a liquidity charge associated with theportfolio; calculating, by the least one processor, a margin requirementor a stress requirement for the portfolio based, at least in part on thespread risk factor, the idiosyncratic risk factor, the interest raterisk factor, and the liquidity risk factor using the margin model or thestress model, respectively; and presenting, by the least one processor,information corresponding to the calculated stress requirement or thecalculated margin requirement.
 20. The method of claim 19, whereincalculating the spread risk factor comprises using a Monte Carlo-basedscenario generator.
 21. The method of claim 19, wherein calculating theinterest rate risk factor comprises: calculating an up-shock lossassociated with an up shock to an interest rate curve used in CDSpricing; calculating a down-shock loss associated with a down shock tothe interest rate curve used in CDS pricing; and calculating theinterest rate risk factor as a maximum of the up-shock loss and thedown-shock loss.